CHAPTER 13 SPHERICAL MIRRORS QUESTIONS AND ANSWERS
1. A spherical concave mirror has a radius of curvature of 52 cm. What is the focal length of the mirror?
Solution
The focal length is half the radius of curvature. So f = 52 ÷ 2 = 26 cm.
2. A concave mirror of focal length 25 cm is used to reflect a real image onto a screen 30 cm away. Calculate the object distance and magnification produced.
Solution
Substitute the values into 1 1
__ u + 1
____ 30 = 1
____ 25 ⇒ 1
__ u = 1
____ 25 − 1
__ u + 1
____ 30 ⇒ 1
__ v = 1
So u = 150 cm Now find the magnification factor:
m = v
__ u = 30
_____ 150 = 0.2
3. A girl uses a concave mirror of 68 cm focal length to apply make-up each morning. If her face is 20 cm from the mirror, what is the image distance? What type of image is produced?
Solution
____ 20 + 1
Substitute the values into 1 1
__ v = 1
____ 68 ⇒ 1
v = −28.3 cm
The minus sign indicates the image is virtual. (We could have avoided this by using a negative sign v in the formula.)
___ v = 1
____ 68 – 1
__ u + 1
____ 20 ⇒ 1
__ v = 1
__ f :
__ v = −0.035
__ f :
__ u = 0.0067
4. A pin 5 cm long held in front of a concave mirror of focal length 20 cm produces an image 20 cm high. Find the object distance if the image is:
(i) (ii) real virtual.
Solution First use m = v
__ u to write u or v in terms of
the other: 4 = v
__ u ⇒ v = 4u
Now substitute 4u for v in the general optics formula.
(i) For a real image, use 1 1
__ u + 1
____ 4u = 1
____ 20 ⇒ 4
____ 4u + 1
____ 4u = 1
__ u + 1
__ v = 1
____ 20 ⇒ 5
This gives 100 = 4u, so u = 25 cm. (ii) For a virtual image, use 1 1
__ u − 1
____ 4u = 1
3
____ 4u = 1
____ 20
This gives 60 = 4u, so u = 15 cm
____ 20 ⇒ 4
____ 4u − 1
____ 4u = 1
____ 20
__ f :
____ 4u = 1
__ u − 1
__ v = 1
____ 20
__ f :
You may now complete Exercise 13A (page 137).
You may now proceed with the mandatory experiment: Measurement of the focal length of a concave mirror (page 427).
